How do rescues and shelters build relationships over long distances?

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I used to foster for a rescue in Maryland and while some of our fosters came from local shelters, quite a few came from rural shelters in other states. Now we moved to Arkansas where the whole dog rescue situation is very different. So my question is, how would I go about creating some sort of relationship with rescues in areas that might be able to take some of the dogs from here? If you are a rescue that pulls from out of state shelters, how did you start? Did the shelter contact the rescue or vice versa? How exactly do you make the whole transport and so on work?
Any info would be great. I am trying to find out as much as possible to be able to give this info to the shelters and hopefully set something up.

I can't help much, but I think the rescue you used to work with might be a good place to start, assuming that relationship ended on good terms. They could probably tell you how to go about it. I'm in kind of a similar situation- I volunteered as a foster for a tiny rescue out West that doesn't have much of an interview questionnaire or do home visits. The previous rescue I worked for was awesome about that stuff, and they were really nice about letting me use their materials. It might be really helpful to just reach out to a few nearby rescues whose philosophies look appealing. You could tell them what kind of behavior testing you're able to do, if any, since a lot of them like to pull young, healthy, friendly dogs, what procedures and cost are involved in their taking the dogs, and whether you guys can do any transport. I think a lot of places make it difficult, so just knowing that you're open to the idea might help a lot.

I had the same issue when I volunteered at a local shelter, too many dogs and no rescues coming in to help.

I talked with the shelter director (to make sure it was okay) and started contacting breed specific rescues for any pure-breeds that we had. Then I started contacting other rescues which take all breeds and mixes. It is hard to get a relationship established as most of the rescues at first will want to pull the younger, healthy dogs. As long as the shelter is okay with that, the relationship will build to the point where the rescues will start taking older harder to adopt dogs.

The main thing is to make sure the shelter staff are willing to work with the rescue as in if a rescue says they want a dog, the staff will hold it (usually for a day) for them and not adopt it out before the rescue can get it (at the shelter I did this for we would have the people fill out a shelter app and give it to the rescue when they pick up the dog).

Also, be sure the shelter is willing to post special events the rescue is having (like if the rescue is having a fundraiser, the shelter puts it on their website). This will help the relationship grow as the rescue will see that the shelter is grateful for the help and hopefully through the rescues event some animals will get adopted and they will come to the shelter to pull more.

I really hope that this helps and that some rescues start helping out the shelter in your area. Good Luck